Question

Differentiate

Answer 1

\[y= c (\cos t)+ t^2sint\]

Answer 2

\[\Large\rm y'=(c\cdot \cos t)'+(t^2 \sin t)'\]\[\Large\rm y'=c(\cos t)'+(t^2 \sin t)'\]Hmm looks like you'll need to apply product rule on that second part, yah?

Answer 3

my worry is actually in the first part c(cost) does the c differentiate to 0

Answer 4

No.
Example: \(\Large\rm \frac{d}{dx}2\cdot x^2 \ne 0\cdot 2x\)
We instead pull the constant out of the differentiation process: \(\Large\rm =2\frac{d}{dx}x^2=2\cdot 2x\)

Answer 5

You COULD do the product rule with c and cos t.
\(\Large\rm (c\cdot\cos t)'=c'\cos t+c(\cos t)'= 0+c(\cos t)'\)
But you'll find that the first term always goes away like that, since one of them is constant.

Answer 6

ok...so will it be
\[y \prime =c(-sint)+t^2cost+2tsint\]

Answer 7

Yay good job \c:/

Answer 8

You could simplify your answer a tad bit by combining like terms... but it's not necessary.

Answer 9

Like you could factor out a sin t and have \(\Large\rm (2t-c)\sin t\) for the sines. but yah don't do that :d not necessary hehe

Answer 10

thanks :)